Answer:
a) v = 2,152 10⁸ m / s b) t = 2.71 10⁸ s or t = 85.93 year
Explanation:
a) In this special relativity exercise we have that time is measured in the same ship, so it is the proper time,
v = d / t
Let's reduce the distance to the SI system
d = 4.3 l and (9.46 1015 m / 1ly) = 40.678 10¹⁵ m
t = 5.0 y (365 day / 1 y) (24 h / 1 day) (3600s / 1h) = 1.89 10⁸ s
Let's calculate
v = 40.678 10¹⁵ / 1.89 10⁸
v = 2,152 10⁸ m / s
b) The time seen from the ground for which the ship moves is given by
t = t₀ / √ (1- (v/c)²)
Let's calculate
t = 1.89 10⁸ / √ (1 - (2.152 / 2.998)²)
t = 1.89 10⁸ / 0.6962
t = 2.71 10⁸ s
Let's reduce this time to years
t = 2.71 10⁸ s (1h / 3600s) (1day / 24h) (1 and / 365 d)
t = 85.93 year
